Does Jesus’ appointment of 12 apostles connect to the 12 tribes of Israel? 

Yes, indeed.

The 12 patriarchs (Levi, Judah, Benjamin, Dan...) were the 12 sons of Jacob, whose covenant name was Israel. Jesus made it clear that the apostles would be the ones in charge in his kingdom (Matt 19:28; Luke 22:30). The church was built on the foundation of the New Testament apostles (Eph 2:20; Rev 21:14) and the New Testament prophets (Eph 2:20; 3:5; 4:11).

Further, in James 1:1 the Christians are called “the twelve tribes.” The church is the extension of Israel, replacing / displacing it, as we are under the new covenant (Hebrews 8).